Sequence

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Introduction

A sequence is one of the earliest and easiest definitions encountered, but I will restate it.

I was taught to denote the sequence {a1,a2,...} by \{a_n\}_{n=1}^\infty however I don't like this, as it looks like a set. I have seen the notation (a_n)_{n=1}^\infty and I must say I prefer it.

Definition

Formally a sequence is a function[1], f:\mathbb{N}\rightarrow S where S is some set. For a finite sequence it is simply f:\{1,...,n\}\rightarrow S

There is little more to say.

Convergence of a sequence

See also

References

  1. Jump up p46 - Introduction To Set Theory, third edition, Jech and Hrbacek